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John deposits $1,000 in an account with annual rate x percent (compoun

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John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025


*A solution will be posted in two days.
[Reveal] Spoiler: OA

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Re: John deposits $1,000 in an account with annual rate x percent (compoun [#permalink]

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New post 31 Jan 2016, 22:30
MathRevolution wrote:
John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025


*A solution will be posted in two days.

Solving statement 1 gives r=4.93, and 2 gives r=4.96.
Both values gives amount>1050.
so answer is D
(i solved this using calculator, kindly explain how to use logic and avoid calculations)

For statement B - time can be considered 1/2 year . by this logic intrest earned in first half year would be grtr than 25 and intrest earned in second half would also be greater than 25. Adding these we will definitely get more than 1050 in a year.

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Re: John deposits $1,000 in an account with annual rate x percent (compoun [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025

When you modify the original condition and the question, they become 1,000(1+x/400)^4>1.050?에서 (1+x/400)^4>1.050/1,000=1.05?. There is 1 variable(x) in the original condition, which should match with the number of equations. Thus, D is likely to be the answer.
In 2), when raising the both equations to the second power, they become (1+x/400)^4>1.025^2=1.050626>1.050, which is yes.
In 1), they become (1+x/400)^4≥ (1+x/200)^2> 1.05, which is always yes. The reason is the quarterly deposit including the rate is bigger than the semi annual deposit including the rate or they’re the same, which is yes. Just like this case, when you’re stuck between A and B when it comes to the mistake type 4(B), consider the answer D.
The answer is D for this question.
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Re: John deposits $1,000 in an account with annual rate x percent (compoun [#permalink]

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New post 09 Feb 2016, 09:59
Both statementes would let you find x and therefore you would be able to find the final balance of the account. There is actually no need to calculate the value you just know it would end up being more or less than $1.050.





sharma123 wrote:
MathRevolution wrote:
John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025


*A solution will be posted in two days.

Solving statement 1 gives r=4.93, and 2 gives r=4.96.
Both values gives amount>1050.
so answer is D
(i solved this using calculator, kindly explain how to use logic and avoid calculations)

For statement B - time can be considered 1/2 year . by this logic intrest earned in first half year would be grtr than 25 and intrest earned in second half would also be greater than 25. Adding these we will definitely get more than 1050 in a year.

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John deposits $1,000 in an account with annual rate x percent (compoun [#permalink]

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MathRevolution wrote:
John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025


Since \(x%\) is anual and the deposit is compounded quarterly, the account balance after one year will be \(1000 \times (1+\frac{x}{4 \times 100})^4 = 1000 \times (1+\frac{x}{400})^4\)

Hence, the question asks whether \(1000 \times (1+\frac{x}{400})^4 > 1050 \iff (1+\frac{x}{400})^4 > 1.05\) (*)

(1) \((1+\frac{x}{200})^2 > 1.05\)

Note that \((1+\frac{x}{400})^2 = 1 + \frac{x}{200} + (\frac{x}{400})^2 > 1 + \frac{x}{200}\)

Hence \((1+\frac{x}{400})^4 > (1+\frac{x}{200})^2 > 1.05\). This means (*) is true. Sufficient.

(2) \((1+\frac{x}{400})^2>1.025 \implies (1+\frac{x}{400})^4>1.025^2 = 1.050625 > 1.05\). Hence, (*) is true, sufficient.

The answer is D.
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John deposits $1,000 in an account with annual rate x percent (compoun [#permalink]

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New post 23 Nov 2017, 22:03
broall wrote:
MathRevolution wrote:
John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025


Since \(x%\) is anual and the deposit is compounded quarterly, the account balance after one year will be \(1000 \times (1+\frac{x}{4 \times 100})^4 = 1000 \times (1+\frac{x}{400})^4\)

Hence, the question asks whether \(1000 \times (1+\frac{x}{400})^4 > 1050 \iff (1+\frac{x}{400})^4 > 1.05\) (*)

(1) \((1+\frac{x}{200})^2 > 1.05\)

Note that \((1+\frac{x}{400})^2 = 1 + \frac{x}{200} + (\frac{x}{400})^2 > 1 + \frac{x}{200}\)

Hence \((1+\frac{x}{400})^4 > (1+\frac{x}{200})^2 > 1.05\).
This means (*) is true. Sufficient.

(2) \((1+\frac{x}{400})^2>1.025 \implies (1+\frac{x}{400})^4>1.025^2 = 1.050625 > 1.05\). Hence, (*) is true, sufficient.

The answer is D.




Hi,
I did not understand the highlighted part. Can you please explain??

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Re: John deposits $1,000 in an account with annual rate x percent (compoun [#permalink]

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New post 24 Nov 2017, 00:37
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Krystallized wrote:
broall wrote:
MathRevolution wrote:
John deposits $1,000 in an account with annual rate x percent (compound quarterly), no other activity for this account, is account balance over $1,050 after one year?

1) (1+x/200)^2> 1.05
2) (1+x/400)^2>1.025


Since \(x%\) is anual and the deposit is compounded quarterly, the account balance after one year will be \(1000 \times (1+\frac{x}{4 \times 100})^4 = 1000 \times (1+\frac{x}{400})^4\)

Hence, the question asks whether \(1000 \times (1+\frac{x}{400})^4 > 1050 \iff (1+\frac{x}{400})^4 > 1.05\) (*)

(1) \((1+\frac{x}{200})^2 > 1.05\)

Note that \((1+\frac{x}{400})^2 = 1 + \frac{x}{200} + (\frac{x}{400})^2 > 1 + \frac{x}{200}\)

Hence \((1+\frac{x}{400})^4 > (1+\frac{x}{200})^2 > 1.05\).
This means (*) is true. Sufficient.

(2) \((1+\frac{x}{400})^2>1.025 \implies (1+\frac{x}{400})^4>1.025^2 = 1.050625 > 1.05\). Hence, (*) is true, sufficient.

The answer is D.


Hi,
I did not understand the highlighted part. Can you please explain??

\((1+\frac{x}{400})^2 = 1 + \frac{x}{200} + (\frac{x}{400})^2 > 1 + \frac{x}{200}\)

We always have \((\frac{x}{400})^2 > 0\) so \(1 + \frac{x}{200} + (\frac{x}{400})^2 > 1 + \frac{x}{200}\)

\((1+\frac{x}{400})^4 > (1+\frac{x}{200})^2 > 1.05\)

Now, \((1+\frac{x}{400})^4 = \Big( (1+\frac{x}{400})^2 \Big) ^2 > (1+\frac{x}{200})^2\)

Now, the statement (1) said that \((1+\frac{x}{200})^2 > 1.05\)
So \((1+\frac{x}{400})^4 > (1+\frac{x}{200})^2 > 1.05\)

Hope this helps.
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Re: John deposits $1,000 in an account with annual rate x percent (compoun   [#permalink] 24 Nov 2017, 00:37
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